Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
4
votes
1 answer

Find the method of moments estimator of theta

Let $Y_1, Y_2, \dots, Y_n$ be i.i.d RVs from the following distribution: $$f(y) = \theta y ^{\theta -1} \qquad 0 < y < 1, \quad\theta > 0$$ Show the method of moment estimator of theta is: $\bar Y/(1-\bar Y)$ I must only be seeing solutions that…
user84756
  • 275
4
votes
1 answer

Is this a mutually exclusive event?

$\begin{array}{|c|c|c|c|} \hline & X = a & X = b & \text{Total} \\ \hline Y = c & 20 & 70 & 90 \\ \hline Y = d & 15 & 45 & 60 \\ \hline \text{Total} & 35 & 115 & 150 \\ …
Talha Abid
  • 83
4
votes
1 answer

Typo in introductory statistics book

Mistake in book. This is an example from an indtroduction to the central limit theorem written by a professor at my university. Is this a typo?
ernesto
  • 549
4
votes
1 answer

Please verify this Proportion Hypothesis Test (Statistics)

Questions: $120$ voters, $39$ identify with radical movement. does this provide sufficient evidence that more than $25\%$ of voters identify with radical movement? use $p$-value approach. My Steps: (0) Check Requirements $(120)(.25)>10$ and…
Patrick
  • 151
  • 2
  • 10
4
votes
2 answers

2 values expected value problem

A bank account has 1000 dollars and get's a 5% interest daily. Every day the account has $0.405$ probability to lose $20$ dollars. What's the mean of the amount of money in the acount after 2 days? I thought about calculating…
Mishe Mitasek
  • 75
4
votes
1 answer

What rating system should I use for a team-based webiste?

My website has a few thousand users, and they play in teams pitted against each other, i.e. 5v5. I want to implement a system whereby each user has an individual rating that adjusts whether they win/lose, depending on the skill rating of the other…
thatbennyguy
  • 43
4
votes
2 answers

What is a 100th percentile?

I am really confused behind the mathematical meaning of a 100th percentile. What does that mean mathematically? Does it mean that a data point in a sample space is greater in some metric and that is also greater than itself? That makes no sense.…
ng.newbie
  • 1,017
  • 1
  • 12
  • 22
4
votes
2 answers

Can a bimodal distribution have a gap?

The question asks to describe the distribution of aspen tree diameters from the sample. I said that the distribution was bimodal with one peak around 5.2 and the other peak around 9.2. However the correct answer is that the distribution is skewed…
user130306
  • 1,890
4
votes
2 answers

Stats 101 - Exam Question Fail, or just tricky to answer?

This appeared on a friends Stats 101 exam: You have a random sample of 2000 respondents who's mean age is 47.3. A friend of yours, (who is knowledgeable about such things) claims that republican voters are, on average, older and…
JHarnach
  • 143
4
votes
1 answer

Hypothesis testing

Suppose we have a random sample $X_1$, $X_2$ from the Beta($\theta$, $1$) distribution and we want to test $H_{\theta} :\theta \leq 1$ against $H_1:\theta > 1$. The following test issued: “Reject $H_0$ if and only if $3X_1 \leq 4X_2$.” How to show…
0x0
  • 2,641
4
votes
2 answers

Optimal sample size?

What's the simplest formula to calculate the optimal sample size from a population size? I've been reading a little about it and they ask me stuff like confidence level or confidence interval which I have no idea about. I need to test some HTML…
Juan
  • 971
4
votes
2 answers

Alterative Sum of Squared Error formula proof

The well-known formula of calculating Sum of Squared Error for a cluster is this: SSE formula where "c" is the mean and "x" is the value of an observation. But this formula also brings the same result: Alternative SSE formula where "m" is the number…
Ian_Lane
  • 43
4
votes
1 answer

What is the median of an empty set?

The median of a singleton set is the element itself. The median of a set with two elements is the average of the elements. What should a machine return when required the median of an empty set?
HAL9000
  • 205
4
votes
1 answer

How do mean and standard deviation change after discarding outliers?

**Sara measured the time in minutes between cars passing her camp near a desert road over a two hour period The times she measured were 6, 6, 8, 9, 10, 11, 13, 13, 20, 24. She calculated the mean and standard deviation for this set of data. (She…
Momen Osama
  • 119
4
votes
3 answers

Probability that $\max(U_1,U_2) > U_3$ for independent uniform random variables $U_i$

Suppose $U_1$, $U_2$ and $U_3$ are independent uniform $(0,1)$. I am supposed to find $P(\max(U_1,U_2) > U_3)$. What I rewrote the question as was this is equal to: $$2P(U_1>U_3) - P(U_1 \mathrm{ and }\,\, U_2 > 3) = 2(1/2) - 1/3 = 2/3.$$ Can…
mary
  • 2,374
1 2 3
…
99 100